3.3: parallel and perpendicular lines
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3.3: Parallel and Perpendicular Lines. There is no spoon. -Spoon Boy and Neo. Relating Parallel and Perpendicular Lines. a. b. c. Theorem 3-9: If two lines are parallel to the same line, then they are parallel to each other. Relating Parallel and Perpendicular Lines. t. m. n. - PowerPoint PPT PresentationTRANSCRIPT
3.3: Parallel and Perpendicular Lines
There is no spoon.-Spoon Boy and Neo
Relating Parallel and Perpendicular Lines
Theorem 3-9: If two lines are parallel to the same line, then they are parallel to each other.
a || b
ab
c
Relating Parallel and Perpendicular Lines
t
m
Theorem 3-10: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
m || n
n
Relating Parallel and Perpendicular Lines
t
m
n
Statements Reasons
1.
2.
3.
4.
1.
2.
3.
4.
12
m t, n t
m || n
Given : m t, n t
Prove : m || n
1 and 2 are
right angles
1
2
Relating Parallel and Perpendicular Lines
ln
Theorem 3-11: In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.
n m
m
Relating Parallel and Perpendicular Lines
ln
m
Statements Reasons
1.
2.
3.
4.
1.
2.
3.
4.
1 is a right
n l, and l || m
Given : n l, and l || m
Prove : n m
1
2
Corresp. ‘s post.
n m
Get busy living, or get busy dying.-Red
3.3: Parallel and Perpendicular Lines
HOMEWORK: p. 140 #51-52, p. 144 #26-27, p. 153 #45-46, Checkpoint Quiz 1 (p. 153) #1-9
Constructing l || m
Given : Line l and point N not on l
Construct : line m through N with m || l
lN
Step 2: Construct with vertex at N so thatand the two angles are corresponding angles. Label this line m.
2
12
Step 1: Label point H on l. Draw HN. Label the angle it makes with l as .
1
Constructing a Special Quadrilateral
Step 1: Construct AZ with length a.
a
Given : Segments of length a and b
Construct : Quadrilateral ABYZ with
AZ a, BY b, and AZ || BY b
Step 2: Draw a point B not on AZ. Then draw AB.
Step 3: Construct a ray parallel to AZ through B.
Step 4: Construct Y so that BY = b. Then draw YZ.
Constructing Perpendicular Lines
lP
Step 1: Put the compass point on point P. Draw arcs intersecting l in two points. Label the points A and B.
Step 2: Open the compass wider. With the compass tip on A, draw an arc above point P.
Given : Point P on line l
Construct : CP with CP l
Step 3: Without changing the compass setting, place the compass point on B. Draw an arc that intersects the previous arc and label the intersection C.
Step 4: Draw CP.
Constructing Perpendicular Lines
l
R
Step 1: Put the compass point on point R. Draw arcs intersecting l in two points. Label the points E and F.
Step 2: Place the compass point in E and make an arc.
Given : line l and Point R not on l
Construct : RG with RG l
Step 3: Without changing the compass setting, place the compass point on F. Draw an arc that intersects the previous arc and label the intersection G.
Step 4: Draw RG.